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Coordinate Systems - SVY21, UTM & the Transverse Mercator Projection

The reference behind this coordinate converter: what a projected grid (Easting/Northing) is, how the Transverse Mercator projection turns latitude/longitude into a plane grid, the exact parameters of SVY21 (Singapore), UTM and VN-2000, and how each converts back to WGS84 latitude/longitude for checking on Google Maps.

🌐Open the interactive coordinate converter→

Run this method in the free calculator and export the result to Excel (.xlsx) or PDF.

A survey coordinate can be written two ways: as geographiclatitude and longitude on a curved ellipsoid, or as a flat projected grid of Easting and Northing in metres. Site plans, setting-out data and GPS receivers all use grids, but every map app speaks latitude/longitude - so converting between them is a daily task. This page explains the projection that connects the two, the exact parameters of SVY21, UTM and VN-2000, and how each converts back to WGS84 for checking on a map.

Ellipsoid (lat/long)(φ, λ)central meridian λ₀TMGrid (E, N)(E, N)E →N →
Transverse Mercator maps latitude/longitude onto a plane Easting/Northing grid, true to scale along the central meridian.

Geographic vs projected coordinates

The Earth is modelled as an ellipsoid - for modern systems the WGS84 ellipsoid, with semi-major axis a=6378137a = 6378137 m and inverse flattening 1/f=298.2572235631/f = 298.257223563. A position on it is given by latitude φ\varphi and longitude λ\lambda. To draw that on a flat plan we project it onto a plane, producing an Easting (EE) and Northing (NN) in metres. No flat map of a curved surface can avoid distortion; a projection simply chooses where to put it.

The Transverse Mercator projection

SVY21, UTM and VN-2000 all use the same projection: Transverse Mercator (TM). It wraps a cylinder around the globe touching a chosen central meridian λ0\lambda_0, then projects the ellipsoid onto it. Scale is true along the central meridian (or reduced by a scale factor k0k_0) and grows with east-west distance from it, so each TM system limits its width. The forward projection uses the Redfearn series; the Easting and Northing are:

E=FE+k0 ν[A+(1−t+c)A36+(5−18t+t2+72c−58e′2)A5120]E = FE + k_0\,\nu\left[A + \tfrac{(1-t+c)A^{3}}{6} + \tfrac{(5-18t+t^{2}+72c-58e'^2)A^{5}}{120}\right]
N=FN+k0[M−M0+νtan⁡φ(A22+(5−t+9c+4c2)A424+⋯ )]N = FN + k_0\left[M - M_0 + \nu\tan\varphi\left(\tfrac{A^{2}}{2} + \tfrac{(5-t+9c+4c^{2})A^{4}}{24} + \cdots\right)\right]

where A=(λ−λ0)cos⁡φA = (\lambda-\lambda_0)\cos\varphi, ν\nu is the radius of curvature in the prime vertical, t=tan⁡2φt = \tan^{2}\varphi, c=e′2cos⁡2φc = e'^2\cos^{2}\varphi, MM is the meridian arc length, and FEFE/FNFN are the false easting/northing. The false values are constants added so grid coordinates stay positive and conveniently sized. The inverse (grid to latitude/longitude) solves for a footpoint latitude by iteration, then applies the reciprocal series - which is exactly what converting Easting/Northing back to lat/long does.

SVY21, UTM and VN-2000 parameters

Because they share the TM formulas, each system is fully described by five numbers - the origin latitude, central meridian, scale factor, false easting and false northing - all on the WGS84 ellipsoid:

SystemOrigin latCentral meridiank₀FE (m)FN (m)
SVY21 (EPSG:3414)1.36666667° N103.833333° E1.028001.64238744.572
UTM zone n (N)0°(6n - 183)°0.99965000000
UTM zone n (S)0°(6n - 183)°0.999650000010000000
VN-2000 (nat.)0°105° E0.99995000000

SVY21 has a scale factor of exactly 1 and a single zone centred on Singapore, so grid distortion across the island is negligible. UTM trades a small scale factor (0.9996) for wider 6-degree zones covering the whole world. VN-2000 is Vietnam's national grid; this tool projects it as TM on WGS84 but does not apply the VN-2000 to WGS84 datum shift, so treat it as approximate (about a metre) for map-checking rather than cadastral work.

Latitude/longitude formats

The same latitude can be written three ways, and survey data mixes them freely:

  • Decimal degrees - e.g. 1.31596∘1.31596^\circ.
  • Degrees and decimal minutes - 1∘18.95′1^\circ 18.95' (the format Singapore's OneMap and this tool show by default).
  • Degrees, minutes, seconds (DMS) - 1∘18′56.99"1^\circ 18' 56.99".

Converting between them is pure arithmetic: minutes are degrees times 60, seconds are minutes times 60. This converter accepts any of the three on input and shows whichever you choose on output, so pasting a DMS value from an API or a decimal-degree value from a GPS both work.

Checking on Google Maps

Google Maps, OpenStreetMap and every web map use WGS84 latitude/longitude - the same datum SVY21 is built on. So once a grid point is converted to lat/long it can be dropped straight onto a map. A quick pin-check catches transposed Easting and Northing, a wrong UTM zone, or a units slip immediately: if the marker lands in the sea or the wrong country, the input was wrong. That is why the converter builds a Google Maps link (and a small preview) for every point.

Web Mercator (EPSG:3857)

The projection the map tiles themselves use is Web Mercator, a spherical Mercator that trades accuracy for speed. Its formulas are simple closed forms on a sphere of radius R=6378137R = 6378137 m:

x=R λ,y=R ln⁡ ⁣[tan⁡ ⁣(π4+φ2)]x = R\,\lambda, \qquad y = R\,\ln\!\left[\tan\!\left(\tfrac{\pi}{4} + \tfrac{\varphi}{2}\right)\right]

It is included for completeness - useful when working with tile pixel coordinates - but it is not a survey grid and should not be used for setting-out.

References

  • Snyder, J.P. (1987). Map Projections - A Working Manual. USGS Professional Paper 1395.
  • Redfearn, J.C.B. (1948). "Transverse Mercator Formulae." Empire Survey Review, 9(69), 318-322.
  • National Imagery and Mapping Agency (2000). Department of Defense World Geodetic System 1984 (WGS 84). NIMA TR8350.2, 3rd edition.
  • Singapore Land Authority (2019). SVY21 - Singapore Plane Coordinate System. Technical specification, SLA.
  • Ministry of Natural Resources and Environment, Vietnam (2000). VN-2000 National Coordinate System. Decision 83/2000/QD-TTg.

Frequently asked questions

SVY21 (EPSG:3414) is a Transverse Mercator projection on the WGS84 ellipsoid, so converting an SVY21 Easting/Northing to latitude/longitude is the inverse projection - no datum shift is needed because SVY21 already uses WGS84. This converter applies the standard Redfearn inverse series with the SVY21 parameters (latitude of origin 1.36666666666667 deg, central meridian 103.833333333333 deg, scale factor 1, false easting 28001.642 m, false northing 38744.572 m). Enter the Easting and Northing and you get the WGS84 latitude/longitude instantly, plus a Google Maps link to check it.

SVY21 / Singapore TM (EPSG:3414) is a Transverse Mercator projection referenced to the WGS84 ellipsoid, with latitude of origin 1.36666666666667 deg N, central meridian 103.833333333333 deg E, scale factor 1.0, false easting 28001.642 m and false northing 38744.572 m. Because the scale factor is exactly 1 and the origin sits near the centre of Singapore, grid distortion across the island is very small.

Transverse Mercator (TM) wraps a cylinder around the Earth touching a chosen central meridian, then projects latitude/longitude onto it to form a flat Easting/Northing grid. Distortion grows with distance east or west of the central meridian, so TM systems limit their width - UTM uses 6-degree zones, and SVY21 uses one zone centred on Singapore. SVY21, UTM and VN-2000 are all the same TM projection with different parameters (central meridian, scale factor, false easting/northing), which is why one engine converts all of them.

Both are Transverse Mercator, but UTM divides the world into sixty 6-degree-wide zones, each with a scale factor of 0.9996, a false easting of 500000 m and (in the southern hemisphere) a false northing of 10000000 m. SVY21 instead uses a single zone tailored to Singapore, with a scale factor of exactly 1 and origin/false values chosen so the grid coordinates stay positive and modestly sized. A point therefore has different Easting/Northing values in UTM and in SVY21, even though both describe the same location on the WGS84 ellipsoid.

Yes, but with a caveat. This tool projects VN-2000 as a Transverse Mercator grid on the WGS84 ellipsoid at a chosen central meridian (105 deg nationally, or a provincial zone), which matches the projection geometry. It does not apply the 7-parameter datum transformation between VN-2000 and WGS84, so results can differ from official VN-2000 coordinates by roughly a metre. For map-checking and approximate work that is fine; for cadastral or setting-out work, use the official transformation parameters.

Google Maps uses WGS84 latitude/longitude, the same datum SVY21 is built on, so a converted point can be dropped straight onto the map to confirm it lands where expected. This is a fast sanity check against transposed Easting/Northing, a wrong zone, or a units mistake - if the pin appears in the sea or in the wrong country, the input was wrong. This converter builds a Google Maps link for every point for exactly this check.

Yes. Switch to Batch mode, then either paste a table of rows or upload a .csv/.xlsx file. The first two columns are read as coordinate A and B (a header row is skipped automatically), every row is converted into all systems, and you can export the result back to CSV or Excel with a Google Maps link per row. This replaces the manual, one-row-at-a-time workflow of a spreadsheet.

Need to convert a point? Enter SVY21, UTM, VN-2000 or lat/long, see it in every system, and open it on Google Maps.

🌐Open the interactive coordinate converter→
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